Showing papers on "Quadrature amplitude modulation published in 1998"

Signal space diversity: a power- and bandwidth-efficient diversity technique for the Rayleigh fading channel

Abstract: The increasing need for high data-rate transmissions over time- or frequency-selective fading channels has drawn attention to modulation schemes with high spectral efficiency such as QAM. With the aim of increasing the "diversity order" of the signal set we consider multidimensional rotated QAM constellations. Very high diversity orders can be achieved and this results in an almost Gaussian performance over the fading channel, This multidimensional modulation scheme is essentially uncoded and enables one to trade diversity for system complexity, at no power or bandwidth expense.

Adaptive coded modulation for fading channels

Abstract: We apply coset codes to adaptive modulation in fading channels. Adaptive modulation is a powerful technique to improve the energy efficiency and increase the data rate over a fading channel. Coset codes are a natural choice to use with adaptive modulation since the channel coding and modulation designs are separable. Therefore, trellis and lattice codes designed for additive white Gaussian noise (AWGN) channels can be superimposed on adaptive modulation for fading channels, with the same approximate coding gains. We first describe the methodology for combining coset codes with a general class of adaptive modulation techniques. We then apply this methodology to a spectrally efficient adaptive M-ary quadrature amplitude modulation (MQAM) to obtain trellis-coded adaptive MQAM. We present analytical and simulation results for this design which show an effective coding gain of 3 dB relative to uncoded adaptive MQAM for a simple four-state trellis code, and an effective 3.6-dB coding gain for an eight-state trellis code. More complex trellis codes are shown to achieve higher gains. We also compare the performance of trellis-coded adaptive MQAM to that of coded modulation with built-in time diversity and fixed-rate modulation. The adaptive method exhibits a power savings of up to 20 dB.

Bandwidth-efficient turbo trellis-coded modulation using punctured component codes

Abstract: We present a bandwidth-efficient channel coding scheme that has an overall structure similar to binary turbo codes, but employs trellis-coded modulation (TCM) codes (including multidimensional codes) as component codes. The combination of turbo codes with powerful bandwidth-efficient component codes leads to a straightforward encoder structure, and allows iterative decoding in analogy to the binary turbo decoder. However, certain special conditions may need to be met at the encoder, and the iterative decoder needs to be adapted to the decoding of the component TCM codes. The scheme has been investigated for 8-PSK, 16-QAM, and 64-QAM modulation schemes with varying overall bandwidth efficiencies. A simple code choice based on the minimal distance of the punctured component code has also been performed. The interset distances of the partitioning tree can be used to fix the number of coded and uncoded bits. We derive the symbol-by-symbol MAP component decoder operating in the log domain, and apply methods of reducing decoder complexity. Simulation results are presented and compare the scheme with traditional TCM as well as turbo codes with Gray mapping. The results show that the novel scheme is very powerful, yet of modest complexity since simple component codes are used.

A space-time coding modem for high-data-rate wireless communications

Abstract: This paper presents the theory and practice of a new advanced modem technology suitable for high-data-rate wireless communications and presents its performance over a frequency-flat Rayleigh fading channel. The new technology is based on space-time coded modulation (STCM) with multiple transmit and/or multiple receive antennas and orthogonal pilot sequence insertion (O-PSI). In this approach, data is encoded by a space-time (ST) channel encoder and the output of the encoder is split into N streams to be simultaneously transmitted using N transmit antennas. The transmitter inserts periodic orthogonal pilot sequences in each of the simultaneously transmitted bursts. The receiver uses those pilot sequences to estimate the fading channel. When combined with an appropriately designed interpolation filter, accurate channel state information (CSI) can be estimated for the decoding process. Simulation results of the proposed modem, as applied to the IS-136 cellular standard, are presented. We present the frame error rate (FER) performance results as a function of the signal-to-noise ratio (SNR) and the maximum Doppler frequency, in the presence of timing and frequency offset errors. Simulation results show that for a 10% FER, a 32-state eight-phase-shift keyed (8-PSK) ST code with two transmit and two receive antennas can support data rates up to 55.8 kb/s on a 30-kHz channel, at an SNR of 11.7 dB and a maximum Doppler frequency of 180 Hz. Simulation results for other codes and other channel conditions are also provided. We also compare the performance of the proposed STCM scheme with delay diversity schemes and conclude that STCM can provide significant SNR improvement over simple delay diversity.

Iterative demapping and decoding for multilevel modulation

Abstract: Iterative decoding algorithms for spectrally efficient modulation have become a vital field of research in digital communications. We show how iterative demapping reduces the bit error rate in conventional communication systems applying multilevel modulation combined with simple channel coding. For this the soft demapping has to be modified in order to accept a priori information. The system can be regarded as a serially concatenated iterative decoding scheme whereby the inner decoder is replaced by the soft demapping device. A design rule based on mutual information to find the 'best' mapping is proposed. Numerical results are presented for 4-PAM and 16-QAM examples.

Impacts Of I/q Imbalance On Qpsk-ofdm-qam Detection

Abstract: The impacts of the I/Q imbalance in the quadrature down-converter on the performance of a QPSK-OFDM-QAM system are studied. Either amplitude or phase imbalance introduces inter-channel interference (ICI). In addition to the ICI, there is a cross-talk between in-phase and quadrature channels in each and every sub-carrier when both amplitude and phase imbalances are present. The BER (bit error ratio) performance of QPSK sub-carriers are also calculated to illustrate the impacts of the I/Q imbalance. It is observed that with the amplitude imbalance less than 1 dB and phase imbalance less than 5 degrees, the degradation of BER performance is less than 0.5 dB for a BER>10/sup -6/.

A hybrid analytical-simulation procedure for performance evaluation in M-QAM-OFDM schemes in presence of nonlinear distortions

Abstract: Presents a hybrid analytical-simulation procedure for performance evaluation in M-ary quadrature amplitude modulation (M-QAM) orthogonal frequency-division multiplexing (OFDM) digital radio systems in the presence of nonlinear distortions caused by high-power amplifiers (HPAs). The present analysis is carried out considering an additive white Gaussian noise (AWGN) transmission channel. It is shown that, in the case of an OFDM system with a large number of subcarriers, the distortion on the received symbol caused by the amplifier can be modeled, with good approximation, as a "Gaussian nonlinear noise" added to the received symbol. This important result allows a hybrid analytical-simulation approach to solve the problem of performance evaluation. In practice, the simulation aspect is only used to estimate means and variances of the "nonlinear noise". Such estimated parameters are subsequently used to evaluate analytically the system bit-error rate (BER) using an expression, which takes into account both AWGN and "nonlinear noise" effects. The advantage of the proposed method lies in the strongly reduced computational time. In fact, an accurate estimate of the "nonlinear noise" parameters requires only few iterations when compared with a classical semianalytical approach. This is especially true when low BER values (<10/sup -4/) have to be estimated. The proposed procedure is applied to evaluate M-QAM-OFDM performance in the presence of nonlinear distortions caused by traveling-wave tube (TWT) and solid-state-power (SSP) amplifiers.

Peak power and bandwidth efficient linear modulation

Abstract: In portable wireless communication systems, power consumption is of major concern. Traditional modulation and coding schemes have been designed from the standpoint of minimizing average power. However, for linear power amplifiers needed for spectrally efficient modulation formats, amplifier efficiency and hence power consumption are determined by the peak power of the transmitted signal. This paper looks into modulation formats which minimize peak power and retain high spectral efficiency. Peak power is broken into a sum (in terms of decibels) of average power and a peak-to-average power ratio, and a variety of modulation formats are evaluated in terms of peak power efficiency in both a Gaussian noise and Rayleigh fading channel. A generalized phase shift keying (PSK) modulation format is developed and shown to offer superior peak power efficiency relative to that of commonly used linear modulation formats. Two schemes are presented for reducing the peak-to-average power ratio of various modulation formats. First, data translation codes are used to avoid data sequences which cause large peaks in the transmitted signal. This approach was found to be most productive in quadrature amplitude modulation (QAM) formats. Finally, an adaptive peak suppression algorithm is presented which further reduces the peak-to-average power ratios of the PSK and generalized PSK formats. The peak suppression algorithm is also applicable to /spl pi//4-QPSK and was found to improve peak power efficiency of that format by about 1.25 dB over a Rayleigh fading channel.

Symbol rate and modulation level-controlled adaptive modulation/TDMA/TDD system for high-bit-rate wireless data transmission

Abstract: This paper proposes a time-division multiple-access/time-division duplex (TDMA/TDD)-based symbol rate and modulation level-controlled adaptive modulation system for high-bit-rate data transmission. The proposed system controls both the symbol rate and modulation level for the next transmission time slot according to the estimated carrier power to noise spectral density ratio (C/N/sub 0/) and delay spread for the time slot to achieve higher bit rate and higher transmission quality as well as higher delay-spread immunity. It is demonstrated by computer simulation and laboratory experiments that the proposed system can achieve a higher average bit rate with higher transmission quality in comparison with the fixed-rate quaternary phase-shift keying (QPSK) system and modulation level-controlled adaptive modulation system in both flat Rayleigh and frequency-selective fading environments. The simulated and experimental results also show that the proposed adaptive modulation techniques can be applied to 1-2-Mb/s indoor and outdoor microcellular systems with its delay spread of up to 250 ns and its terminal mobility of up to pedestrian speed without employing any special antifrequency-selective fading techniques, such as the adaptive equalizer and space diversity.

A method for communicating information in a communication system that supports multiple modulation schemes

Abstract: A method of communicating control information in systems that support multiple modulation schemes for communicating voice or data and control information. To provide backward compatibility dedicated control channels use the modulation scheme used in current systems, for example GMSK modulation scheme. Traffic channels and associated control channels use linear modulation schemes that have the same symbol rate. The modulation scheme of the associated control channel uses a reduced signal set of the modulation scheme used for traffic channels. Also, an in-band signalling procedure is used to indicate to a receiving station the modulation type, channel coding and speech coding used for a transmitted burst.

Performance analysis of Viterbi decoding for 64-DAPSK and 64-QAM modulated OFDM signals

Abstract: The multilevel modulation techniques of 64-quadrature amplitude modulation (QAM) and 64-differential amplitude and phase-shift keying (DAPSK) have been proposed in combination with the orthogonal frequency-division multiplexing (OFDM) scheme for digital terrestrial video broadcasting (DTVB). With this system a data rate of 34 Mb/s can be transmitted over an 8-MHz radio channel. A comparison of these modulation methods in the uncoded case has been presented by Engels and Rohling (see European Trans. Telecommun., vol.6, p.633-40, 1995). The channel coding scheme proposed for DTVB by Schafer (see Proc. Int. Broadcasting Convention, Amsterdam, The Netherlands, p.79-84, 1995) consists of an inner convolutional code concatenated with an outer Reed-Solomon (RS) code. In this paper the performance of the convolutional codes is analyzed for the two modulation techniques. This analysis includes soft decision Viterbi (1971) decoding of the convolutional code. For soft decision decoding of DAPSK modulated signals a new metric is developed.

Ethernet transport facility over digital subscriber lines

Abstract: A facility transport system for transporting Ethernet over digital subscriber lines. The system, termed 10BaseS, is capable of transmitting of 10 Mbps Ethernet over existing copper infrastructure. The system utilizes carrierless amplitude modulation phase modulation/quadrature amplitude modulation (CAP/QAM) to transport Ethernet frame data and utilizes splitter means (22) to separate both the downstream and upstream channels from POST signals.

Radio interface performance of EDGE, a proposal for enhanced data rates in existing digital cellular systems

Abstract: The use of alternative modulation to provide Enhanced Data rates for Global Evolution (EDGE) is currently being standardized for GSM by the European Telecommunications Standards Institute (ETSI), and is also adopted for IS-136 evolution by the Universal Wireless Communications Consortium (UWCC) in the USA. In this paper, the currently proposed radio interface for this concept and first link simulation results are presented. It is demonstrated that high-level modulation is feasible with an acceptable increase of complexity, and provides good performance, even if impacts like power amplifier nonlinearity, phase noise, frequency offset etc. are taken into account,.

Error probability performance of L-branch diversity reception of MQAM in Rayleigh fading

Abstract: New exact expressions involving hypergeometric functions are derived for the symbol-error rate (SER) of M-ary quadrature amplitude modulation (MQAM) for L branch diversity reception in Rayleigh fading and additive white Gaussian noise (AWGN). The diversity combining techniques considered are maximum ratio combining (MRC) and selection combining (SC). MRC with identical channels and dissimilar channels are analyzed.

Direct multilevel carrier modulation using millimeter-wave balanced vector modulators

Abstract: The importance of being able to design affordable, high-performance, millimeter-wave transmitters for digital communications and radar applications is increasing. To this end, two monolithic millimeter-wave vector modulators have been realized at 38 and 60 GHz for use in direct multilevel carrier modulation. It is shown that, by employing balanced biphase amplitude modulator elements, accurate constellations are achieved with broad-band operation from 20 to 40 GHz and 55 to 65 GHz. Modulations of 16- and 256-QAM have been demonstrated, both at 38 and 60 GHz, using this technique. Each balanced biphase amplitude modulator uses a pair of reflection-type attenuators operated in push-pull mode. This study investigates the suitability of this topology for use as a full biphase amplitude modulator for multilevel digital modulation schemes. It is found that the technique is very robust and the resulting analog vector modulator can be a very important component for many future millimeter-wave applications.

TCM/SSMA communication systems with cascaded sequences and PAM/QAM signal sets

Abstract: An expression in matrix form for the multiple-access interference (MAI) in an asynchronous direct-sequence spread-spectrum multiple-access (DS/SSMA) communication system with cascaded sequences (CVs), arbitrary chip waveforms, and trellis-coded modulation (TCM) with a pulse amplitude modulation (PAM) or quadrature amplitude modulation (QAM) signal set is obtained. TCM provides significant coding gain while the CVs decrease the correlation between the MAI of adjacent data intervals. The expression is used to calculate arbitrarily accurate probability density functions (PDFs) of the MAI in the TCM system and to derive an accurate approximation of the MAI variance. It also helps illustrate some properties of the MAI by separating contributing parameters into different matrices. We derive an approximation of the upper union bound on the bit-error probability and investigate its applicability. The results show that CV schemes can greatly reduce the pairwise error probabilities (PEPs) until the length of the CV becomes greater than that of the error weight sequence (EWS) under consideration.

OFDM performance in amplifier nonlinearity

Abstract: The activities of the current European RACE and ACTS projects have led to an increasing interest in OFDM (orthogonal frequency division multiplexing) as a means of combating impulsive noise and multipath effects and making fuller use of the available bandwidth of the system. This paper analyses the performance of OFDM signals in amplifier nonlinearity. In particular, bit error rate (BER) degradation as a result of amplitude limiting or clipping are analysed. In the presence of both nonlinear distortion and additive Gaussian noise, optimized output power back off is provided to balance the requirements of minimum BER and power amplifier efficiency. For this purpose, an OFDM system has been built using the SPW (Signal Processing Worksystem) simulator.

Comparison of single-carrier and multitone digital modulation for ADSL applications

Abstract: Single-carrier modulation such as quadrature amplitude modulation (QAM) or carrierless amplitude modulation-phase modulation (CAP), and DMT are alternative techniques for providing digital communication in a variety of applications, in particular ADSL for communication over the telephone company subscriber lines. Although theory predicts comparable performance under ideal implementations, a definitive comparison of performance over a wide range of conditions will require more experience from field trials. Similarly, accurate comparison of implementation costs must await the greater availability of commercial-grade devices. However, enough is now known about these modulation schemes to compare their inherent similarities and differences in performance and cost. Overall, a present view of single-carrier and multitone modulation indicates comparable performance with some differences depending on the type of degradation. Costs should also be approximately equal, with multitone having some advantage in digital processing, but requiring greater cost in analog circuitry.

FM-DCSK: a novel method for chaotic communications

Abstract: In binary Differential Chaos Shift Keying (DCSK), each information bit is mapped to the correlation between two pieces of a chaotic waveform. The receiver determines the correlation (which is proportional to the energy per bit) in order to demodulate the received signal. Since a chaotic signal is not periodic, the energy per bit is not constant and can only be estimated, even in the noise-free case. This estimation has a non-zero variance that limits the attainable data rate. This problem can be avoided if the energy per bit is kept constant. In this paper, the DCSK technique is combined with frequency modulation in order to achieve two properties: the excellent noise performance of DCSK is maintained; in addition, the energy per bit is kept constant in order not to limit the data rate. A low-pass equivalent model that significantly speeds up the simulation of an FM-DCSK system is also developed. Finally the noise performance of the proposed FM-DCSK system is given.

Single-channel blind equalization for GSM cellular systems

Abstract: This paper focuses on the study of blind equalization global system for mobile communications (GSM) systems using a single antenna. In order to utilize the well-known linear system model in conventional studies of blind equalization, an equivalent baseband quadrature amplitude modulation (QAM) approximation is used for the nonlinear GMSK signal in GSM systems. Since the GMSK signal in GSM has very little excess bandwidth to warrant oversampling, a derotation scheme is developed to create two subchannels for each received GMSK signal sampled at the baud rate. Linear approximation of the GMSK signal makes the traditional QAM blind equalization system model applicable for GSM. Derotation induces channel diversity without an additional antenna and reduces the number of necessary radio frequency (RF) receivers (sensors) without increasing hardware or computational costs. Several second-order statistical and higher order statistical methods of blind equalization are adopted for GSM signals.

Method and apparatus for transmitting and receiving digital data over a bandpass channel

Abstract: A method and apparatus for transmitting and receiving acquired digital data over bandpass channels (i.e. channels having a limited range of frequencies) at high data transmission rates. Combined amplitude and phase modulation (quadrature amplitude modulation) is applied to the digital data and the sampled digital waveform converted to an analog waveform for passage over the bandpass channel. The sample rate is chosen as an integer multiple of the symbol rate and carrier frequency to significantly reduce processing overhead. Reception of the acquired data is similar to transmission and involves an analogous amplitude and phase demodulation. The quadrature amplitude modulation technique of the present invention is applied to an oil well-logging application to transmit the data acquired from the downhole logging instruments over the logging cable (bandpass channel) at high transmission rates.

Variable rate adaptive trellis coded QAM for high bandwidth efficiency applications in Rayleigh fading channels

Abstract: A high bandwidth efficiency variable rate adaptive channel coding scheme, ATCQAM, is proposed. Known pilot symbols are transmitted periodically to aid demodulation. Past channel states are fed back to the transmitter with delay. Current channel state is then predicted at the transmitter to decide on the appropriate modulation mode for the current symbol. At good channel states, high level modulation is used to boost up the average throughput. At bad channel states, low level modulation is used to increase error protection. By matching the variable modulation level with a variable rate channel coder, the physical bandwidth is maintained constant. Design issues for the ATCQAM are considered. The effects of finite feedback delay, finite interleaving depth and mobile speed are investigated.

Multiple hypothesis modulation classification based on cyclic cumulants of different orders

Abstract: A multiple hypothesis modulation QAM classification task is addressed. The classifier is designed within the rigorous framework of decision theory. A characteristic feature is extracted from the signal, and is compared to the possible theoretical features in the maximum likelihood sense. This feature is composed of a combination between fourth-order and squared second-order cyclic temporal cumulants. No assumption about the power of the signal is made. It is shown that this uncertainty about the power of the signal does not affect the decision rule. As an application, we present simulated performance in the context of 4-QAM vs 16-QAM vs 64-QAM classification.

Filtered decision feedback channel estimation for OFDM-based DTV terrestrial broadcasting system

Abstract: Orthogonal frequency division multiplexing (OFDM) is one of the transmission techniques used for digital television (DTV) terrestrial broadcasting. A high quality channel estimator with a low training overhead is the key to the successful delivery of DTV services which require high spectrum efficiency and robustness to strong and dynamic ghosts. Robustness to multipath distortion is especially important in a single frequency emission environment. This paper presents an application of a filtered decision feedback channel estimator for OFDM-based DTV systems using high order QAM modulations. The implementation and the performance of the channel estimator are discussed. Computer simulations were conducted to evaluate the performance of the channel estimator. The channel estimation loss is about 1.2 dB from the ideal case where the channel is assumed to be known by the receiver. For a given multipath spread, the loss can be further reduced by increasing the FFT size. The FFT size is however subject to an upper limit imposed by the Doppler spread.

Reduced complexity equalizer for multi mode signaling

Abstract: A transmission channel equalizer system may be used to process either signals that have been modulated according to quadrature amplitude modulation (QAM) or vestigial sideband modulation (VSB) to convey digital symbols. The equalizer system includes a sparse digital filter having coefficients which are adaptively updated. The filter system includes a finite impulse response (FIR) filter which processes modulated pass-band RF signals and an infinite impulse response (IIR) filter which processes demodulated base-band signals. At least one of the FIR and IIR filters is implemented as a sparse filter. The filter system is responsive to a control signal to switch between processing QAM and VSB signals. The update algorithm for the equalizer employs a constant modulus algorithm (CMA) to acquire the digital signal and a decision directed (DD) algorithm to track the digital signal. The CMA algorithm used when VSB signals are processed is a single axis CMA (SACMA) algorithm. The filter converts the VSB signal into a pseudo QAM signal before the slicing operation which recovers the symbols from the converted VSB signal. The slicer identifies an encoded VSB symbol by partial trellis decoding and quantization from a reduced-set constellation.

A general maximum likelihood framework for modulation classification

Abstract: This paper deals with modulation classification. First, a state of the art is given which is separated into two classes: the pattern recognition approach and the maximum likelihood (ML) approach. Then we propose a new classifier called the general maximum likelihood classifier (GMLC) based on an approximation of the likelihood function. We derive equations of this classifier in the case of linear modulation and apply them to the MPSK/M'PSK problem. We show that the new tests are a generalisation of the previous ones using the ML approach, and don't need any restriction on the baseband pulse. Moreover the GMLC provides a theoretical foundation for many empirical classification systems including those systems that exploit the cyclostationary property of modulated signals.

Hardware nonlinearities in digital TV broadcasting using OFDM modulation

Abstract: FFT-based coded orthogonal frequency division multiplexing (COFDM) is one of the techniques for digital TV broadcasting over multipath fading channels. A FFT-based OFDM signal is subject to various hardware nonlinearities in both the transmitter and receiver. Hardware nonlinearities not only affect the in-band performance of an FFT-based OFDM system but also may affect the system performance of an adjacent channel signal because of regenerated sidelobes of the transmitted signal. The paper investigates the in-band and out-of-band behaviour of a 64QAM-OFDM system under various nonlinear devices. It is shown that the inherent signal clipping in the IFFT processors with a limited word length reduces the required RF amplifier output backoff (OBO) where adjacent channel interference is the limiting factor. For a 0.25% clipping rate, an additional 2 dB OBO is required for the COFDM signal to achieve the same level of adjacent channel interference as for the single carrier system. The loss in SNR due to signal clipping is negligible in a coded OFDM system.

Upper bounds on the bit-error rate of optimum combining in wireless systems

Abstract: This paper presents upper bounds on the bit-error rate (BER) of optimum combining in wireless systems with multiple cochannel interferers in a Rayleigh fading environment. We present closed-form expressions for the upper bound on the bit-error rate with optimum combining, for any number of antennas and interferers, with coherent detection of BPSK and QAM signals, and differential detection of DPSK. We also present bounds on the performance gain of optimum combining over maximal ratio combining. These bounds are asymptotically tight with decreasing BER, and results show that the asymptotic gain is within 2 dB of the gain as determined by computer simulation for a variety of cases at a 10/sup -3/ BER. The closed-form expressions for the bound permit rapid calculation of the improvement with optimum combining for any number of interferers and antennas, as compared with the CPU hours previously required by Monte Carlo simulation. Thus these bounds allow calculation of the performance of optimum combining under a variety of conditions where it was not possible previously, including analysis of the outage probability with shadow fading and the combined effect of adaptive arrays and dynamic channel assignment in mobile radio systems.

An asymptotic optimal algorithm for modulation classification

Abstract: A suboptimal algorithm for modulation classification was proposed for classifying the modulation type of general M-ary phase-shifted keying (MPSK) signals. Yang and Soliman (see IEEE Trans. Aerosp. Electron. Syst., vol.33, no.1, p.38-45, 1997) approximated the phase probability density function of a received signal to be the Tikhonov function. Instead, we employ the exact phase density function and derive an asymptotic optimal classification algorithm. We show a structure of this proposed classifier for continuous wave (CW), binary phase-shift keying (BPSK), quaternary phase-shift keying (QPSK), and 8PSK. Besides, we give an example to demonstrate the capability of this algorithm and compare its performance to that in Yang and Soliman. It is shown that the performance is more effective.

Digital modulation classification using power moment matrices

Abstract: With the rising number of modulation types used in multi-user and multi-service digital communication systems, the need to find efficient methods for their discrimination in the presence of noise has become increasingly important. We present a new approach based on a pattern recognition method previously applied to word spotting problems in binary images. In this approach, a large number of spatial moments are arranged in a symmetric positive definite matrix for which eigendecomposition and noise subspace processing methods can be applied. The resultant denoised moment matrix has entries which are used in place of the raw moments for improved pattern classification. In this paper, we generalize the moment matrix technique to grey scale images and apply the technique to discrimination between M-ary PSK and QAM constellations in signal space. Invariance to unknown phase angle and signal amplitude is achieved by representing the in-phase and quadrature components of the signal in the complex plane, and computing joint moments of normalized magnitude and phase components.